Assignment #2

Question 1 (a) How much money will Kevin need at retirement? (12 points) EAR = .10 = [1 + (APR / 12)]12 – 1; EAR = .07 = [1 + (APR / 12)]12 – 1; APR = 12[(1.10)1/12 – 1] = .0957 or 9.57% APR = 12[(1.07)1/12 – 1] = .0678 or 6.78%

PVA = $20,000{1 – [1 / (1 + .0678/12)12(25)]} / (.0678/12) = $2,885,496.45 PV = $900,000 / [1 + (.0678/12)]300 = $165,824.26 $2,885,496.45 + 165,824.26 = $3,051,320.71 (b) How much will he have to save each month in years 11 through 30? (20 points) His savings after 10 years: FVA = $2,500[{[ 1 + (.0957/12)]12(10) – 1} / (.0957/12)] = $499,659.64 After he purchases the cabin: $499,659.64 – 380,000 = $119,659.64 When he is ready to retire, this amount will have grown to: FV = $119,659.64[1 + (.0957/12)]12(20) = $805,010.23 When he is ready to retire, based on his current savings, he will be short: $3,051,320.71 – 805,010.23 = $2,246,310.48 This amount is the FV of the monthly savings he must make between years 10 and 30. So, finding the annuity payment using the FVA equation, we find his monthly savings will need to be: FVA = $2,246,310.48 = C[{[ 1 + (.1048/12)]12(20) – 1} / (.1048/12)]  C = $3,127.44

Question 2. (18 points) a. The payback period for each project is: A: 3 + ($180,000/$390,000) = 3.46 years B: 2 + ($9,000/$18,000) = 2.50 years The payback criterion implies accepting project B, because it pays back sooner than project A. b. The discounted payback for each project is: A: $20,000/1.15 + $50,000/1.152 + $50,000/1.153 = $88,074.30 $390,000/1.154 = $222,983.77 Discounted payback = 3 + ($390,000 – 88,074.30)/$222,983.77 = 3.95 years B: $19,000/1.15 + $12,000/1.152 + $18,000/1.153 = $37,430.76 $10,500/1.154 = $6,003.41 Discounted payback = 3 + ($40,000 – 37,430.76)/$6,003.41 = 3.43 years The discounted payback criterion implies accepting project B because it pays back sooner than A. c. The NPV for each project